Allometric cascade as a unifying principle of body mass effects on metabolism

Problems of allometric scaling analysis: examples from mammalian reproductive biology

Biological scaling analyses employing the widely used bivariate allometric model are beset by at least four interacting problems: (1) choice of an appropriate best-fit line with due attention to the influence of outliers; (2)objective recognition of divergent subsets in the data (allometric grades);(3) potential restrictions on statistical independence resulting from phylogenetic inertia; and (4) the need for extreme caution in inferring causation from correlation. A new non-parametric line-fitting technique has been developed that eliminates requirements for normality of distribution,greatly reduces the influence of outliers and permits objective recognition of grade shifts in substantial datasets. This technique is applied in scaling analyses of mammalian gestation periods and of neonatal body mass in primates. These analyses feed into a re-examination, conducted with partial correlation analysis, of the maternal energy hypothesis relating to mammalian brain evolution, which suggests links between body size and brain size in neonates and adults, gestation period and basal metabolic rate. Much has been made of the potential problem of phylogenetic inertia as a confounding factor in scaling analyses. However, this problem may be less severe than suspected earlier because nested analyses of variance conducted on residual variation(rather than on raw values) reveals that there is considerable variance at low taxonomic levels. In fact, limited divergence in body size between closely related species is one of the prime examples of phylogenetic inertia. One common approach to eliminating perceived problems of phylogenetic inertia in allometric analyses has been calculation of `independent contrast values'. It is demonstrated that the reasoning behind this approach is flawed in several ways. Calculation of contrast values for closely related species of similar body size is, in fact, highly questionable, particularly when there are major deviations from the best-fit line for the scaling relationship under scrutiny.

Modeling of vascular networks

Vascular networks refer here mainly to the microscale capillary networks of the vascular system of mammals, although they may also be considered to include the small arteries that feed the capillaries and the small veins that drain them. The modeling of these networks for resting mammals is reviewed within the context of describing related scaling laws for mammals of vastly different size. Basic processes are considered and alternative approaches mentioned. All lead to the same scaling laws for the radius, length and number of the vessels. The applicability of the relations is illustrated using existing measurements. Discussion is also included on the effect of strenuous exercise on the scaling law for number of capillary vessels and matters related to it.

Multi-level regulation and metabolic scaling

Metabolic control analysis has revealed that flux through pathways is the consequence of system properties, i.e. shared control by multiple steps, as well as the kinetic effects of various pathways and processes over each other. This implies that the allometric scaling of flux rates must be understood in terms of properties that pertain to the regulation of flux rates. In contrast,proponents of models considering the scaling of branching or fractal-like systems suggest that supply rates determine metabolic rates. Therefore, the allometric scaling of supply alone provides a sufficient explanation for the allometric scaling of metabolism. Examination of empirical data from the literature of comparative physiology reveals that basal metabolic rates (BMR)are driven by rates of energy expenditure within internal organs and that the allometric scaling of BMR can be understood in terms of the scaling of the masses and metabolic rates of internal organs. Organ metabolic rates represent the sum of tissue metabolic rates while, within tissues, cellular metabolic rates are the outcome of shared regulation by multiple processes. Maximal metabolic rates (MMR, measured as maximum rates of O2 consumption, V̇O2max) during exercise also scale allometrically, are also subject to control by multiple processes, but are due mainly to O2 consumption by locomotory muscles. Thus, analyses of the scaling of MMR must consider the scaling of both muscle mass and muscle energy expenditure. Consistent with the principle of symmorphosis, allometry in capacities for supply (the outcome of physical design constraints) is observed to be roughly matched by allometry in capacities for demand (i.e. for energy expenditure). However, physiological rates most often fall far below maximum capacities and are subject to multi-step regulation. Thus, mechanistic explanations for the scaling of BMR and MMR must consider the manner in which capacities are matched and how rates are regulated at multiple levels of biological organization.

Bridging the Gap between mesoscopic and macroscopic models: the case of multicellular tumor spheroids

Multicellular tumor spheroids are valuable experimental tools in cancer research. By introducing an intermediate model, we have been able to successfully relate mesoscopic and macroscopic descriptions of spheroid growth. Since these descriptions stem from completely different roots (cell dynamics, and energy conservation and scaling arguments, respectively), their consistency validates both approaches and allows us to establish a direct correspondence between parameters characterizing processes occurring at different scales. Our approach may find applications as an example of bridging the gap between models at different scale levels in other contexts.

Appropriate interpretation of aerobic capacity: allometric scaling in adult and young soccer players

OBJECTIVE

To compare aerobic capacity of young and adult elite soccer players using appropriate scaling procedures.

METHODS

Twenty four male adult (mean (SD) age 24 (2) years, weight 75.7 (7.2) kg, VO2max 66.6 (5.2) ml/lbm/min, where lbm is lean body mass in kg) and 21 youth (14 (0.4) years, 60.2 (7.3) kg, 66.5 (5.9) ml/lbm/min) elite soccer players took part in the study. Allometric equations were used to determine the relation between maximal and submaximal oxygen cost of running (running economy) and body mass.

RESULTS

Maximal and submaximal oxygen uptake increased in proportion to body mass raised to the power of 0.72 (0.04) and 0.60 (0.06) respectively. The VO2max of adult players was similar to that of the youth players when expressed in direct proportion to body mass--that is, ml/kg/min--but 5% higher (p<0.05) when expressed using appropriate procedures for scaling. Conversely, compared with seniors, youth players had 13% higher (p<0.001) energy cost of running--that is, poorer running economy--when expressed as ml/kg/min but not when expressed according to the scaling procedures.

CONCLUSIONS

Compared with the youth soccer players, VO2max in the seniors was underestimated and running economy overestimated when expressed traditionally as ml/lbm/min. The study clearly shows the pitfalls in previous studies when aerobic capacity was evaluated in subjects with different body mass. It further shows that the use of scaling procedures can affect the evaluation of, and the resultant training programme to improve, aerobic capacity.

Hochachka's "Hypoxia Defense Strategies" and the development of the pathway for oxygen

Hochachka's "Hypoxia Defense Strategies" identify oxygen signalling, metabolic arrest, channel arrest and coordinated suppression of ATP turnover rates as key factors that determine the ability of organisms to survive exposure to chronic hypoxia. In this review, I assess the developmental role played by these phenomena in the morphogenesis of the gas exchange tissues that define the pathway for oxygen transport to cytochrome c oxidase. Key areas of regulation lie in: (I) the suppression of fetal mitochondrial oxidative function in hand with mitochondrial biogenesis (metabolic arrest), (II) the role of hypoxia-driven oxygen signalling pathways in directing the scope of non-differentiated stem cell proliferation in placenta and lung development and (III) the regulation of epithelial fluid secretion/absorption in the lung through the oxygen-dependent modulation of Na+ conductance pathways. The identification of developmental roles for Hochachka's "Hypoxia Defense Strategies" in directing the morphogenesis of gas exchange structures bears with it the implication that these strategies are fundamental to establishing the scope for aerobic metabolic performance throughout life.

PETER HOCHACHKA: Adventures in Biochemical Adaptation

Peter Hochachka was one of the most creative forces in the field of comparative physiology during the past half-century. His career was truly an exploratory adventure, in both intellectual and geographic senses. His broad comparative studies of metabolism in organisms as diverse as trout, tunas, oysters, squid, turtles, locusts, hummingbirds, seals, and humans revealed the adaptable features of enzymes and metabolic pathways that provide the biochemical bases for diverse lifestyles and environments. In its combined breadth and depth, no other corpus of work better illustrates the principle of "unity in diversity" that marks comparative physiology. Through his publications, his stimulating mentorship, his broad editorial services, and his continuous-and highly infectious-enthusiasm for his field, Peter Hochachka served as one of the most influential leaders in the transformation of comparative physiology.

Walking on inclines: energetics of locomotion in the antCamponotus

To assess energetic costs during rest and locomotion in a small insect, we measured metabolic rate in freely moving ants Camponotus sp.(average body mass 11.9 mg). The animals ran in a straight respirometric chamber in which locomotor speed and CO2 release were monitored simultaneously using flow-through respirometry and conventional video analysis. In resting intact ants, standard metabolic rate was on average 0.32 ml CO2 g-1 body mass h-1. During walking, the ants breathed continuously and metabolic rate increased between 4.3 times(level walking at 0-5 mm s-1) and 6.9 times (30° ascent at 85-95 mm s-1) over resting rates. Metabolic rate increased linearly with increasing walking speed but superficially leveled off beyond speeds of about 70 mm s-1. Walking on incline (uphill) or decline slopes(downhill) of up to 60° had only a small effect on energy consumption compared to level walking. During slope walking, total metabolic rate averaged over all running speeds ranged from a minimum of 1.55±0.4 (horizontal running) to a maximum of 1.89±0.7 ml CO2 h-1g-1 body mass (30° downhill). The mean cost of transport in Camponotus was approximately 130 J g-1 km-1. The metabolic requirements in the comparatively small insect Camponotus for walking were mostly in the range expected from data obtained from other insects and small poikilotherms, and from allometric scaling laws.

The effect of fasting on activity and resting metabolism in the sand cricket, Gryllus firmus: a multivariate approach

Heat increment of feeding (HIF) is a ubiquitous feature of animals, and corresponds to a conspicuous rise in metabolism after a meal, induced by the release of energy due to digestion and absorption of foodstuffs. However, there exists great variation both in the duration and magnitude of HIF. In insects, HIF is well known, and it appears to be dramatic, especially in immature stages. However, little is known about the effect of HIF on different aspects of metabolism. We determined metabolic rate as CO2 production in fasted and non-fasted nymphs of the sand cricket (Gryllus firmus). A number of metabolic variables were computed from the simultaneous activity record: activity, resting, minimum, maximum and average metabolic rate. Our results suggest that there is a general effect of fasting in metabolic rate but with a graded response: the larger the influence of activity on the metabolic variable, the less is the effect of fasting that was detected.

Control of maximum metabolic rate in humans: dependence on performance phenotypes

Borrowing from metabolic control analysis the concept of control coefficients or ci values, defined as fractional change in MMR/fractional change in the capacity of any given step in ATP turnover, we used four performance phenotypes to compare mechanisms of control of aerobic maximum metabolic rate (MMR): (i) untrained sedentary (US) subjects, as a reference group against which to compare (ii) power trained (PT), (iii) endurance trained (ET), and (iv) high altitude adapted native (HA) subject groups. Sprinters represented the PT group; long distance runners illustrated the ET group; and Andean natives represented the HA group. Numerous recent studies have identified contributors to control on both the adenosine triphosphate (ATP) supply side and the ATP demand side of ATP turnover. From the best available evidence it appears that at MMR all five of the major steps in energy delivery (namely, ventilation, pulmonary diffusion, cardiac output, tissue capillary--mitochondrial O2 transfer, and aerobic cell metabolism per se) approach an upper functional ceiling, with control strength being distributed amongst the various O2 flux steps. On the energy demand side, the situation is somewhat simplified since at MMR approximately 90% of O2-based ATP synthesis is used for actomyosin (AM) and Ca2+ ATPases; at MMR these two ATP demand rates also appear to be near an upper functional ceiling. In consequence, at MMR the control contributions or ci values are distributed amongst all seven major steps in ATP supply and ATP demand pathways right to the point of fatigue. Relative to US (the reference group), in PT subjects at MMR control strength shifts towards O2 delivery steps (ventilation, pulmonary diffusion, and cardiac output); here physiological regulation clearly dominates MMR control. In contrast in ET and HA subjects at MMR control shifts towards the energy demand steps (AM and Ca2+ ATPases), and more control strength is focussed on tissue level ATP supply and ATP demand. One obvious advantage of the ET and HA biochemical-level control is improved metabolite homeostasis. Additionally, with some reserve capacity in the O2 delivery steps, the focussing of control on ATP turnover at the tissue level has allowed nature to improve on an 'endurance machine' design.

Effects of voluntary wheel running and amino acid supplementation on skeletal muscle of mice

The aims of the present study were as follows: (1) to examine the adaptational changes to chronic endurance voluntary exercise and (2) to investigate the effects of amino acid supplementation on the adaptational changes induced by endurance training in hindlimb (gastrocnemius, tibialis, soleus) and respiratory (diaphragm) muscles of mice. Male C57Bl6 mice were divided in four groups: control sedentary, sedentary supplemented with amino acid mixture (BigOne, 1.5 mg g day(-1) in drinking water for 8 weeks), running (free access to running wheels for 8 weeks), and running supplemented with amino acid mixture. Myosin heavy chain (MHC) isoform distribution was determined in all muscles considered. Fiber cross-sectional area (CSA) was measured in the soleus muscle. In all muscles except the tibialis, endurance training was associated with an overall shift towards the expression of slower MHC isoforms. Amino acid supplementation produced a shift towards the expression of faster MHC isoforms in the soleus and diaphragm muscles, and partially antagonized the effects of training. Immunohistochemical analysis of CSA of individual muscle fibers from the soleus muscle suggests that voluntary running produced a decrease in the size of type 1 fibers, and amino acid supplementation during training resulted in an increase in size in both type 1 and type 2A fibers. Collectively, these results suggest that the endurance adaptations induced by voluntary running depend on the muscle type, and that amino acid supplementation is able to modulate both fiber size and MHC isoform composition of skeletal muscles in sedentary and exercised mice.

Metabolic scaling: consensus or controversy?

Background

The relationship between body mass (M) and standard metabolic rate (B) among living organisms remains controversial, though it is widely accepted that in many cases B is approximately proportional to the three-quarters power of M.

Results

The biological significance of the straight-line plots obtained over wide ranges of species when B is plotted against log M remains a matter of debate. In this article we review the values ascribed to the gradients of such graphs (typically 0.75, according to the majority view), and we assess various attempts to explain the allometric power-law phenomenon, placing emphasis on the most recent publications.

Conclusion

Although many of the models that have been advanced have significant attractions, none can be accepted without serious reservations, and the possibility that no one model can fit all cases has to be more seriously entertained.

Metabolic scaling: a many-splendoured thing

Animals at rest and during exercise display rates of aerobic metabolism, VO2, that represent mainly the sum of mitochondrial respiration rates in various organs. The relative contributions of these organs change with physiological state such that internal organs such as liver, kidney and brain account for most of the whole-body VO2 at rest, while locomotory muscles account for >90% of the maximum rate, VO2max, during maximal aerobic exercise. Mechanisms that regulate VO2 are complex and the relative importance of each step in a series, estimated by metabolic control analysis, depends upon the level of biological organization under consideration as well as physiological state. Despite this complexity, prominent single-cause models propose that metabolic rates are supply-limited and that the scaling of supply systems provides a sufficient explanation for the allometric scaling of metabolism. We argue that some assumptions, as well as current interpretations of the meaning (or consequences) of these constraints are flawed, i.e., elephants do not have lower mass-specific basal or maximal rates of aerobic metabolism because their mitochondria are more supply-limited than those of shrews. Animals do not violate the laws of physics, and the allometric scaling of supply systems would be expected, to some extent, to be matched by capacities for (and rates of) energy expenditure. But life is not so simple. Animals are so diverse that to do justice to metabolic scaling, it is also necessary to consider the scaling of energy expenditure. It is by doing so that models of metabolic scaling can be consistent with current paradigms in metabolic regulation and accommodate the range of inter- and intraspecific exponents found in nature. The "allometric cascade," a first attempt at such an accounting, was a source of great satisfaction to Peter Hochachka. It was the last door that he helped open to comparative physiologists before he said goodbye.

Basal Metabolic Rate: History, Composition, Regulation, and Usefulness

The concept of basal metabolic rate (BMR) was developed to compare the metabolic rate of animals and initially was important in a clinical context as a means of determining thyroid status of humans. It was also important in defining the allometric relationship between body mass and metabolic rate of mammals. The BMR of mammals varies with body mass, with the same allometric exponent as field metabolic rate and with many physiological and biochemical rates. The membrane pacemaker theory proposes that the fatty acid composition of membrane bilayers is an important determinant of a species BMR. In both mammals and birds, membrane polyunsaturation decreases and monounsaturation increases with increasing body mass and a decrease in mass-specific BMR. The secretion and production of thyroid hormones in mammals are related to body mass, with the allometric exponent similar to BMR; yet there is no body size-related variation in either total or free concentrations of thyroid hormones in plasma of mammals. It is suggested that in different-sized mammals, the secretion/production of thyroid hormones is a result of BMR differences rather than their cause. BMR is a useful concept in some situations but not in others.

Adventures in oxygen metabolism

Peter W. Hochachka led a grand life of science adventure and left as his legacy a whole new field--biochemical adaptation. Oxygen was at the core of Peter's career and his laboratory made major contributions to our understanding of how animals deal with variation in oxygen availability in many forms. He analyzed the molecular mechanisms that support facultative anaerobiosis, studied muscle exercise metabolism for high speed flight, swimming and running, investigated mammalian diving on many trips to the Antarctic to study Weddell seals, and probed the metabolic and genetic adaptations that provide optimal hypoxia tolerance for humans residing at high altitudes. His work illuminated both biochemical and physiological mechanisms that are used to optimize aerobic metabolism, to compensate for hypoxic insults, and to conserve energy by strong metabolic rate depression under anoxia. His articles, books and lectures galvanized the field with leading-edge insights and theories and he consistently challenged comparative biochemists to use their unique model systems to explore the range and breadth of animal strategies of biochemical adaptation. Lessons drawn from my training in Peter's laboratory have led me on continuing explorations of adaptations in enzyme function, signal transduction, gene expression, and antioxidant defenses ranging over systems of anoxia tolerance, freezing survival, estivation, and mammalian hibernation.

Plant allometry: is there a grand unifying theory?

The study of size and its biological consequences--alled allometry--has fascinated biologists for centuries. Recent advances in this area of study have stimulated a renewed interest in these scaling phenomena, especially in terms of the search for mechanistic explanations that transcend mere descriptive phenomenology. These advances are reviewed in the context of plant biology. Allometric derivations are presented that predict how annual growth in total body biomass is partitioned to construct new leaf, stem, and root tissues at the level of an individual plant. Derivations are also presented to predict annual reproductive effort and to predict how the biomass of body parts changes as a function of the number of plants per unit area in communities. The predictions emerging from these derivations are then examined empirically by comparing predicted and observed scaling exponents for each relationship using a world-wide data compendium gathered from the primary literature. These comparisons provide strong statistical support for each of the allometric predictions. This support is taken as evidence that a general unifying allometric theory for plant biology is near at hand. Nevertheless, the validation of this theory requires much additional work and raises a number of procedural and conceptual concerns that must be resolved before a single 'global' theory is accepted.

Metabolic adaptation to hypoxia: cost and benefit of being small

Following metabolic size allometry, the specific metabolic rate of mammals increases with decreasing body mass, resulting in a steeper metabolic fall-off and a faster exhaustion of energy reserves under hypoxic conditions. However, both mammalian hibernators and fetuses are able to temporarily "switch-off" Kleiber's rule as an adaptation to limited food or oxygen supply. Further exceptions to the usual metabolic size relationship are observed in newborn mammals. For instance, neonatal mouse hearts exhibit slower calorimetric "dying curves" under conditions of ischemia, although their aerobic tissue metabolic rates are higher than in adult samples. This is apparently due to a transient reduction of metabolic rate back to the former feto-maternal level. A continuing deviation from metabolic size allometry is found in newborn marsupials (Monodelphis domestica) where the "inappropriately" low specific metabolic rate is a precondition of efficient growth and tissue aerobiosis in spite of extreme immaturity. Obviously, adaptive suppression of elevated metabolism in organisms of small size results in a dramatic improvement of oxygen supply. Vice-versa, the overall increase in specific metabolic rate with decreasing body size might be regarded as one of several phylogenetic adaptations to protect tissues from hyperoxygenation.

Temperature effects on a whole metabolic reaction cannot be inferred from its components

Changes in temperature affect the kinetic energy of the constituents of a system at the molecular level and have pervasive effects on the physiology of the whole organism. A mechanistic link between these levels of organization has been assumed and made explicit through the use of values of organismal Q10 to infer control of metabolic rate. To be valid this postulate requires linearity and independence of the isolated reaction steps, assumptions not accepted by all. We address this controversy by applying dynamic systems theory and metabolic control analysis to a metabolic pathway model. It is shown that temperature effects on isolated steps cannot rigorously be extrapolated to higher levels of organization.

Respiration rate of hepatocytes varies with body mass in birds

Hepatocytes were isolated from eight species of birds ranging from 13 g zebra finches to 35 kg emus. This represents a 2800-fold range of body mass (Mb). Liver mass (g) was allometrically related to species body mass by the equation: liver mass=19.6 x Mb(0.91). There was a significant allometric decline in hepatocyte respiration rate (HRR; nmol O2 mg(-1) dry mass min(-1)) with species body mass (kg) described by the relationship: HRR=5.27 x Mb(-0.10). The proportions of hepatocyte oxygen consumption devoted to (i) mitochondrial ATP production, (ii) mitochondrial proton leak and (iii) non-mitochondrial processes were estimated by using excess amounts of appropriate inhibitors. It was found that although hepatocyte respiration rate varied with body mass in birds, these processes constitute a relatively constant proportion of hepatocyte metabolic rate irrespective of the size of the bird species. The respective percentages were 54%, 21% and 25%. The portion of hepatocyte respiration devoted to ATP production for use by the sodium pump was estimated and found to be a relatively constant 24% of hepatocyte respiration and 45% of mitochondrial ATP production in different-sized bird species. These results are discussed in the context of competing theories to explain the metabolism-body size allometry, and are found to support the 'allometric cascade' model.

[Biology of size and gravity]

Gravity is a force that acts on mass. Biological effects of gravity and their magnitude depend on scale of mass and difference in density. One significant contribution of space biology is confirmation of direct action of gravity even at the cellular level. Since cell is the elementary unit of life, existence of primary effects of gravity on cells leads to establish the firm basis of gravitational biology. However, gravity is not limited to produce its biological effects on molecules and their reaction networks that compose living cells. Biological system has hierarchical structure with layers of organism, group, and ecological system, which emerge from the system one layer down. Influence of gravity is higher at larger mass. In addition to this, actions of gravity in each layer are caused by process and mechanism that is subjected and different in each layer of the hierarchy. Because of this feature, summing up gravitational action on cells does not explain gravity for biological system at upper layers. Gravity at ecological system or organismal level can not reduced to cellular mechanism. Size of cells and organisms is one of fundamental characters of them and a determinant in their design of form and function. Size closely relates to other physical quantities, such as mass, volume, and surface area. Gravity produces weight of mass. Organisms are required to equip components to support weight and to resist against force that arise at movement of body or a part of it. Volume and surface area associate with mass and heat transport process at body. Gravity dominates those processes by inducing natural convection around organisms. This review covers various elements and process, with which gravity make influence on living systems, chosen on the basis of biology of size. Cells and biochemical networks are under the control of organism to integrate a consolidated form. How cells adjust metabolic rate to meet to the size of the composed organism, whether is gravity responsible for this feature, are subject we discuss in this article. Three major topics in gravitational and space biology are; how living systems have been adapted to terrestrial gravity and evolved, how living systems respond to exotic gravitational environment, and whether living systems could respond and adapt to microgravity. Biology of size can contribute to find a way to answer these question, and answer why gravity is important in biology, at explaining why gravity has been a dominant factor through the evolutional history on the earth.

Aerobic fitness is associated with cardiomyocyte contractile capacity and endothelial function in exercise training and detraining

BACKGROUND

Physical fitness and level of regular exercise are closely related to cardiovascular health. A regimen of regular intensity-controlled treadmill exercise was implemented and withdrawn to identify cellular mechanisms associated with exercise capacity and maximal oxygen uptake (VO2max).

METHODS AND RESULTS

Time-dependent associations between cardiomyocyte dimensions, contractile capacity, and VO2max were assessed in adult rats after high-level intensity-controlled treadmill running for 2, 4, 8, and 13 weeks and detraining for 2 and 4 weeks. With training, cardiomyocyte length, relaxation, shortening, Ca2+ decay, and estimated cell volume correlated with increased VO2max (r=0.92, -0.92, 0.88, -0.84, 0.73; P<0.01). Multiple regression analysis identified cell length, relaxation, and Ca2+ decay as the main explanatory variables for VO2max (R2=0.87, P<0.02). When training stopped, exercise-gained VO2max decreased 50% within 2 weeks and stabilized at 5% above sedentary controls after 4 weeks. Cardiomyocyte size regressed in parallel with VO2max and remained (9%) above sedentary after 4 weeks, whereas cardiomyocyte shortening, contraction/relaxation- and Ca2+-transient time courses, and endothelium-dependent vasorelaxation regressed completely within 2 to 4 weeks of detraining. Cardiomyocyte length, estimated cell volume, width, shortening, and Ca2+ decay and endothelium-dependent arterial relaxation all correlated with VO2max (r=0.85, 0.84, 0.75, 0.63, -0.54, -0.37; P<0.01). Multiple regression identified cardiomyocyte length and vasorelaxation as the main determinants for regressed VO2max during detraining (R2=0.76, P=0.02).

CONCLUSIONS

Cardiovascular adaptation to regular exercise is highly dynamic. On detraining, most of the exercise-gained aerobic fitness acquired over 2 to 3 months is lost within 2 to 4 weeks. The close association between cardiomyocyte dimensions, contractile capacity, arterial relaxation, and aerobic fitness suggests cellular mechanisms underlying these changes.

Emergence of power laws from partitional dynamics

This work explores the possibility of producing some specific power laws (with exponential cut-off) out from a partitional dynamics. The data obtained from the partitions of integers in the interval 1-60 have been used to find the coefficients of a power law and its exponential cut-off, and also of a single hyperbolic form after renormalization. There is also the speculation that this type of power law, so easily derived from arithmetic minimalist operations, may underlie the communication exchanges of living cells and the structural games of self-constructing agents endowed with relative structural freedom.

Allometric scaling of maximal metabolic rate in mammals: muscle aerobic capacity as determinant factor

Maximal metabolic rate (MMR) of mammals scales differently from basal metabolic rate (BMR). This is first shown by scrutinizing data reported on exercise-induced Vo2 max in 34 eutherian mammalian species covering a body mass range of 7 g-500 kg. Vo2 max was found to scale with the 0.872 (+/-0.029, 95% confidence limits 0.813-0.932) power of body mass which is significantly different from the 3/4 power reported for basal metabolic rate. The aerobic scope is higher in athletic than non-athletic species, and it is also higher in large than in small species. Integrated structure-function studies on a subset of 11 species (body mass 20 g-450 kg) show that the variation of Vo2 max with body size is tightly associated with the aerobic capacity of the locomotor musculature: the scaling exponents for Vo2 max, the total volume of mitochondria, and the volume of capillaries are nearly identical. The higher Vo2 max of athletic species is tightly linked to proportionally larger mitochondrial and capillary volumes in animals of the same size class. As a result Vo2 max is linearly related to both total mitochondrial and capillary erythrocyte volumes. We conclude that the scaling of maximal metabolic rate is explained by features and mechanisms different from those determining basal metabolic rate.

The Allometry of Avian Basal Metabolic Rate: Good Predictions Need Good Data

Basal metabolic rate (BMR) is often predicted by allometric interpolation, but such predictions are critically dependent on the quality of the data used to derive allometric equations relating BMR to body mass (Mb). An examination of the metabolic rates used to produce conventional and phylogenetically independent allometries for avian BMR in a recent analysis revealed that only 67 of 248 data unambiguously met the criteria for BMR and had sample sizes with n>/=3. The metabolic rates that represented BMR were significantly lower than those that did not meet the criteria for BMR or were measured under unspecified conditions. Moreover, our conventional allometric estimates of BMR (W; logBMR=-1.461+0.669logMb) using a more constrained data set that met the conditions that define BMR and had n>/=3 were 10%-12% lower than those obtained in the earlier analysis. The inclusion of data that do not represent BMR results in the overestimation of predicted BMR and can potentially lead to incorrect conclusions concerning metabolic adaptation. Our analyses using a data set that included only BMR with n>/=3 were consistent with the conclusion that BMR does not differ between passerine and nonpasserine birds after taking phylogeny into account. With an increased focus on data mining and synthetic analyses, our study suggests that a thorough knowledge of how data sets are generated and the underlying constraints on their interpretation is a necessary prerequisite for such exercises.

Embryogenesis and oxygen consumption in benthic egg clutches of a tropical clownfish, Amphiprion melanopus (Pomacentridae)

Variation in size at hatching is common in demersal spawning organisms, suggesting that processes during embryonic development may be critical in determining growth and development. To examine critical periods during embryonic development in the demersal spawning reef fish Amphiprion melanopus, the rate of oxygen consumption within an egg clutch was compared to morphological changes in the embryos. Oxygen consumption was least on day 1 of development where organ differentiation had not begun (mean 1.73+/-0.34x10(-5) micromol O(2) egg(-1) s(-1)). Tail movement throughout the perivitelline fluid began on day 3 and is likely to assist in moving oxygen around the embryo, complementing diffusive transport. The appearance of haemoglobin in the blood corresponded to a peak in oxygen consumption on day 4, where the highest mean rate of oxygen consumption was recorded (6.73+/-0.82x10(-5) micromol O(2) egg(-1) s(-1)). This could be a critical period in development whereby risk of mortality is increased through increased embryo requirements at developmental thresholds.

Scaling behavior of VO2peak in trained wheelchair athletes

PURPOSE

To examine the scaling behavior of peak oxygen uptake (VO2peak) in wheelchair athletes, adjusting for known covariates.

METHODS

Body mass, VO2peak, and an estimate of adiposity (sum of four skinfolds) were determined in a sample of 45 highly trained wheelchair basketball and racing athletes. The participants were classified as possessing either "high" or "low" trunk stability and balance using recognized sporting classifications. A wheelchair ergometer was used to obtain the VO2peak measurements. The relationship between VO2peak and body mass was obtained via a nonlinear allometric model with the sum of four skinfolds, trunk stability and balance, and chronological age entered as covariates.

RESULTS

The point estimate exponent for body mass was 0.82 (95% CI, 0.54-1.10). After controlling for the influence of body mass, adiposity, and age, the wheelchair athletes with greater trunk stability and balance had on average an 11% greater VO2peak. The regression model explained 54% of the sample variance in VO2peak.

CONCLUSIONS

The obtained mass exponent of 0.82 is congruent with that predicted from the multiple-causes allometric cascade model and consideration of the physiological characteristics of spinal cord injured athletes. To compare the body size-independent VO2peak values of athletes within the study sample, the mass exponent of 0.82 may be adopted (i.e., mL x kg(-0.82) x min(-1)). The uncertainty in the point estimate, reflected in the relatively wide 95% CI, highlights the need for further research with larger samples to increase the precision of estimation.

Intraspecific Relationships between Resting and Activity Metabolism in Anuran Amphibians: Influence of Ecology and Behavior

The aerobic capacity model, as well as other models for the evolution of aerobic metabolism and the origin of endothermy, requires a mechanistic link between rates of resting and activity oxygen consumption (VO2rest and VO2act). The existence of such link is still controversial, but studies with anuran amphibians support a correlation between VO2rest and VO2act at both the intraspecific and interspecific levels. Because results at the intraspecific level are based only on a few species, we test for the generality of a link between these two metabolic variables in anurans by studying the intraspecific correlational patterns between mass-independent VO2rest and VO2act in anurans. We focus on 21 Neotropical species from different geographical areas that include remarkable diversity in behavior and thermal ecology. Although uncorrelated, VO2rest and VO2act seem to be consistent among individuals. Diverse intraspecific phenotypic correlational trends were detected, indicating that the intraspecific relationships between VO2rest and VO2act might be very diverse in anurans. The three possible trends (positive, negative, and absent correlations) were observed and appeared to be predictable from ecological and behavioral variables that relate to evolutionary physiological shifts in anurans. Positive correlations between VO2rest and VO2act were more common in species with active lifestyles (e.g., intense vocal activity) and in species that call at low temperatures (e.g., winter or high-elevation specialists).

Cold-acclimation inPeromyscus: temporal effects and individual variation in maximum metabolism and ventilatory traits

Thermal acclimation in small endotherms provides an excellent model for the study of physiological plasticity, as energy requirements can be easily manipulated and the results are relevant for natural conditions. Nevertheless,how physiology changes throughout acclimation, and how individuals vary in their response to acclimation, remain poorly understood. Here we describe a high temporal-resolution study of cold acclimation in the deer mouse Peromyscus maniculatus. The experimental design was based on repeated measures at short intervals throughout cold acclimation, with controls(maintained at constant temperature) for measurement artifacts. We monitored body mass, maximum metabolic rate in cold exposure and ventilatory traits(respiratory frequency, tidal and minute volume and oxygen extraction) for 3 weeks at 23°C. Then, half of the individuals were held for 7 weeks at 5°C. Body mass was differently affected by cold acclimation depending on sex. Maximal metabolism(V̇O2max)increased significantly during the first week of cold acclimation, `overshot'after 5 weeks and dropped to a plateau about 34% above control values at week 7. Similarly, ventilatory traits increased during cold acclimation, though responses were different in their kinetics and magnitude. Body mass, maximum metabolism, and most ventilatory traits were repeatable after 7 weeks in control and cold-acclimated animals. However, repeatability tended to be lower in the cold-acclimated group, especially while animals were still acclimating. Our results show that acclimation effects may be under- and/or overestimated,depending on when trials are performed, and that different traits respond differently, and at different rates, to acclimation. Hence, future studies should be designed to ensure that animals have attained steady-state values in acclimation experiments.

Are adult physiques geometrically similar? The dangers of allometric scaling using body mass power laws

Human physique classification by somatotype assumes that adult humans are geometric similar to each other. However, this assumption has yet to be adequately tested in athletic and nonexercising human populations. In this study, we assessed this assumption by comparing the mass exponents associated with girth measurements taken at 13 different sites throughout the body in 478 subjects (279 athletic subjects, and 199 nonexercising controls). Corrected girths which account for subcutaneous adipose tissue at the upper arm, thigh, and calf sites, and which simulate muscle circumference, were also calculated. If subjects are geometrically similar to each other, girth exponents should be approximately proportional to M(1/3), where M is the subjects' body mass. This study confirms that human adult physiques are not geometrically similar to each other. In both athletic subjects and nonexercising controls, body circumferences/limb girths develop at a greater rate than that anticipated by geometric similarity in fleshy sites containing both muscle and fat (upper arms and legs), and less than anticipated in bony sites (head, wrists, and ankles). Interestingly, head girths appear to remain almost constant, irrespective of subjects' body size/mass. The results also suggest that thigh muscle girths of athletes and controls increase at a greater rate than that predicted by geometric similarity, proportional to body mass (M(0.439) and M(0.377), respectively). These systematic deviations from geometric similarity have serious implications for the allometric scaling of variables such as energy expenditure, oxygen uptake, anaerobic power, and thermodynamic or anthropometric studies involving individuals of differing size.

A definition of internal constancy and homeostasis in the context of non-equilibrium thermodynamics

The constancy of the internal environment, internal homeostasis, and its stability are necessary conditions for the survival of a biological system within its environment. These have never been clearly defined. For this purpose nonequilibrium thermodynamics is taken as a reference, and the essential principles of equilibrium, reversibility, stationary steady state and stability (Lyapounov, asymptotic, local and global), are briefly illustrated. On this basis, internal homeostasis describes a stationary state of nonequilibrium, the actual state of rest, X(t), resulting from the relation X(t) = Xs + x(t), between a time-independent steady state of reference (Xs), and time-dependent fluctuations of the state variables, x(t). In humans, two resting spontaneous homeostatic states are: (1) the conscious state of quiet wakefulness, during which time-dependent variables display bounded oscillations around the mean time-independent steady state level, this conscious state being thus stable in the sense of Lyapounov, and (2) the unconscious stable state of non-rapid eye movement sleep, in which the time-dependent variables would approach the lowest spontaneously attainable time-independent state asymptotically, sleep becoming a globally stable and attractive state. Exercise may be described as a non-resting, unstable active state far away from equilibrium and hibernation is a resting, time-independent steady state very near equilibrium. The range between sleep and exercise is neurohumorally regulated. For spontaneously stable states to occur, slowing of the metabolic rate, withdrawal of the sympathetic drive and reinforcement of the vagal tone to the heart and circulation are required, thus confirming that the parasympathetic division of the autonomic nervous system is the main controller of homeostasis.

Cell size as a link between noncoding DNA and metabolic rate scaling

Accumulation of noncoding DNA and therefore genome size (C-value) may be under strong selection toward increase of body size accompanied by low metabolic costs. C-value directly affects cell size and specific metabolic rate indirectly. Body size can enlarge through increase of cell size and/or cell number, with small cells having higher metabolic rates. We argue that scaling exponents of interspecific allometries of metabolic rates are by-products of evolutionary diversification of C-values within narrow taxonomic groups, which underlines the participation of cell size and cell number in body size optimization. This optimization leads to an inverse relation between slopes of interspecific allometries of metabolic rates and C-value. To test this prediction we extracted literature data on basal metabolic rate (BMR), body mass, and C-value of mammals and birds representing six and eight orders, respectively. Analysis of covariance revealed significant heterogeneity of the allometric slopes of BMR and C-value in both mammals and birds. As we predicted, the correlation between allometric exponents of BMR and C-value was negative and statistically significant among mammalian and avian orders.

Endosymbiosis and the design of eukaryotic electron transport

The bioenergetic organelles of eukaryotic cells, mitochondria and chloroplasts, are derived from endosymbiotic bacteria. Their electron transport chains (ETCs) resemble those of free-living bacteria, but were tailored for energy transformation within the host cell. Parallel evolutionary processes in mitochondria and chloroplasts include reductive as well as expansive events: On one hand, bacterial complexes were lost in eukaryotes with a concomitant loss of metabolic flexibility. On the other hand, new subunits have been added to the remaining bacterial complexes, new complexes have been introduced, and elaborate folding patterns of the thylakoid and mitochondrial inner membranes have emerged. Some bacterial pathways were reinvented independently by eukaryotes, such as parallel routes for quinol oxidation or the use of various anaerobic electron acceptors. Multicellular organization and ontogenetic cycles in eukaryotes gave rise to further modifications of the bioenergetic organelles. Besides mitochondria and chloroplasts, eukaryotes have ETCs in other membranes, such as the plasma membrane (PM) redox system, or the cytochrome P450 (CYP) system. These systems have fewer complexes and simpler branching patterns than those in energy-transforming organelles, and they are often adapted to non-bioenergetic functions such as detoxification or cellular defense.

Patterns of control of maximum metabolic rate in humans

In this analysis, four performance phenotypes were used to compare mechanisms of control of aerobic maximum metabolic rate (MMR): (i) untrained sedentary (US) subjects, as a reference group against which to compare (ii) power trained (PT), (iii) endurance trained (ET) and (iv) high altitude adapted native (HA) subject groups. Sprinters represented the PT group; long distance runners illustrated the ET group; and Quechuas represented the HA group. Numerous recent studies have identified contributors to control on both the adenosine triphosphate (ATP) supply side and the ATP demand side of ATP turnover. Control coefficients or c(i) values were defined as fractional change in MMR/fractional change in the capacity of any given step in ATP turnover. From the best available evidence it appears that at MMR all five of the major steps in energy delivery (namely, ventilation, pulmonary diffusion, cardiac output, tissue capillary - mitochondrial O(2) transfer, and aerobic cell metabolism per se) approach an upper functional ceiling, with control strength being distributed amongst the various O(2) flux steps. On the energy demand side, the situation is somewhat simplified since at MMR approximately 90% of O(2)-based ATP synthesis is used for actomyosin (AM) and Ca(2+) ATPases; at MMR these two ATP demand rates also appear to be near an upper functional ceiling. In consequence, at MMR the control contributions or c(i) values are rather evenly divided amongst all seven major steps in ATP supply and ATP demand pathways right to the point of fatigue. Relative to US (the reference group), in PT subjects at MMR control strength shifts towards O(2) delivery steps (ventilation, pulmonary diffusion and cardiac output). In contrast in ET and HA subjects at MMR control shifts towards the energy demand steps (AM and Ca(2+) ATPases), and more control strength is focussed on tissue level ATP supply and ATP demand. One obvious advantage of the ET and HA control pattern is improved metabolite homeostasis. Another possibility is that, with some reserve capacity in the O(2) delivery steps and control focussed on ATP turnover at the tissue level, nature has designed the ideal 'endurance machine'.

Subspecies and body size allometry affect milk production and composition, and calf growth in red deer: comparison of Cervus elaphus hispanicus and Cervus elaphus scoticus

Studies comparing lactation in wild mammals have shown that maternal weight scales with offspring weight, milk production, or its energy. However, no study appears to have scaled milk composition with maternal or offspring weight. Although diet affects milk composition and production, their effects in biological studies have almost never seemed to be controlled. In this study, we compare two subspecies of red deer, Scottish deer, Cervus elaphus scoticus (10 lactations), and Iberian deer, Cervus elaphus hispanicus (14 lactations), kept under the same diet and housing to assess differences in hind and calf weights and their trends, milk production and composition, and their allometric relationships. Scottish hinds were heavier, and calf weight and gains were greater than Iberian ones, with greater milk production and milk protein content, but they did not differ in fat or lactose content. Calf birth weight, milk production, and protein content showed significant allometric relationships with maternal weight, but no relationship was found for fat, lactose, or any of these variables with calf birth weight. Protein content correlated with calf birth weight, and calf weight trend depended on milk protein production rather than on that of fat or lactose. Protein may be the most important milk component to explain growth and milk composition differences between closely related mammals.

Switching of metabolic-rate scaling between allometry and isometry in colonial ascidians

The metabolic rate and its scaling relationship to colony size were studied in the colonial ascidian Botrylloides simodensis. The colonial metabolic rate, measured by the oxygen consumption rate (V(O2) in millilitres of O(2) per hour) and the colony mass (wet weight M(w) in grams) showed the allometric relationship (V(O2) = 0.0412 M(w)(0.799). The power coefficient was statistically not different from 0.75, the value for unitary organisms. The size of the zooids and the tunic volume fraction in a colony were kept constant irrespective of the colonial size. These results, together with the two-dimensional colonial shape, excluded shape factors and colonial composition as possible causes of allometry. Botryllid ascidians show a takeover state in which all the zooids of the parent generation in a colony degenerate and zooids of a new generation develop in unison. The media for connection between zooids such as a common drainage system and connecting vessels to the common vascular system experienced reconstruction. The metabolic rate during the takeover state was halved and was directly proportional to the colonial mass. The scaling thus changed from being allometric to isometric. The alteration in the scaling that was associated with the loss of the connection between the zooids strongly support the hypothesis that the allometry was derived from mutual interaction among the zooids. The applicability of this hypothesis to unitary organisms is discussed.

Basal rate of metabolism and temperature regulation in Goeldi's monkey (Callimico goeldii)

Basal rate of metabolism (BMR) and temperature regulation are described for Goeldi's monkey (Callimico goeldii), a threatened New World primate species of the family Callitrichidae. Measurements were conducted on sleeping individuals during the night, using a special nestbox designed to serve as a respirometry chamber, such that test animals remained undisturbed in their customary surroundings. Oxygen consumption was measured at ambient temperatures between 17.5 and 32 degrees C for 10 individuals with an average body mass of 557 g. Average BMR was 278+/-41 ml O(2) h(-1), which is lower than the value predicted on the basis of body mass. Individual differences in BMR were significant even when body mass was accounted for. Body temperature was measured in five individuals below thermoneutrality and averaged 36+/-0.3 degrees C. The corresponding thermal conductance averaged 29.3+/-2.2 ml O(2) h(-1) degrees C(-1), which is similar to the expected value. The metabolic and thermoregulatory patterns observed in C. goeldii resemble those of the closely related marmosets and tamarins. Low BMR is presumably associated with limited access to energy resources and may be directly linked with phylogenetic dwarfing in the family Callitrichidae.

The size-independent oxygen cost of running

PURPOSE

The purpose of this investigation was to determine whether differences in running economy among children, adolescents, and adults can be explained by differences in resting metabolism, mass, and stature.

METHODS

Participants were 36 children, 23 adolescents, and 24 adults. Mass-specific gross oxygen cost per minute ([OV0312]O(2gross) x M-1), mass-specific gross oxygen cost per kilometer (VO(2gross) x M-1), mass-specific net oxygen cost per kilometer (VO(2net) x M-1), and a dimensionless index called the size-independent cost (SIC) were compared for level treadmill running at speeds ranging from 1.6 to 3.1 m.s-1. SIC was defined as the net oxygen cost to move a mass of 1 kg a distance equal to stature (mL x kg-1).

RESULTS

Children generally had higher [OV0312]O(2gross).M-1, VO(2gross) x M-1, and VO(2net) x M-1 than adolescents who similarly had greater costs than adults. When SIC was used to control for size-related differences in resting metabolism, mass and stature the costs of children and adults were similar (0.323 +/- 0.034 and 0.338 +/- 0.035 mL x kg-1, respectively, P = 0.54). However, adolescents had significantly higher SIC (0.360 +/- 0.026 mL x kg-1, P < 0.001) than both children and adults. Analysis of data from the literature indicated SIC peaks around 15 yr of age and changes were parallel to changes in the ratio of leg length to stature.

CONCLUSIONS

We conclude that when resting metabolism and the dimensional effects of mass and stature are controlled, the running economy of adolescents is greater than in children and adults, which are similar. Therefore, differences in [OV0312]O(2gross) x M-1, VO(2gross) x M-1, and VO(2net) x M-1 among children, adolescents, and adults do not solely reflect qualitative differences in running performance.

Validity of the allometric cascade model at submaximal and maximal metabolic rates in exercising men

The dependence of metabolic rate (MR) on body mass (M) is described by the general allometric equation MR=aM(b), where, a is a proportionality coefficient and b is the mass exponent. Darveau et al. [Nature 417 (2002), 166] proposed a novel 'multiple-causes' allometric cascade model as a unifying principle of the scaling of MR, at rest and during maximal exercise. We tested the validity of body mass exponents predicted from the model for submaximal and maximal aerobic exercise conditions in 1629 men. MRs were estimated from whole-body oxygen consumption during an incremental treadmill test to voluntary exhaustion. For both submaximal (b=0.83) and maximal (b=0.94) exercise requiring average oxygen consumption rates of around 5-11 times resting values, respectively, the obtained mass exponents were remarkably consistent with predicted values. Moreover, for maximal MR the global mass exponent was significantly greater than for submaximal aerobic metabolism, congruent with the allometric cascade model.

Scaling laws for capillary vessels of mammals at rest and in exercise

A general derivation is presented for the scaling laws governing the size and number of capillary blood vessels in mammals. The derivation is based on the assumption of three idealized similarity principles known to apply, at least approximately, to resting mammals: (i) size-invariant blood pressure; (ii) size-invariant fraction of blood in the capillaries; and (iii) size-invariant oxygen consumption and uptake, per unit of body mass, during each heart cycle. Results indicate that the radius and length of capillaries, and the number that are open and active in the resting state, should scale with mammal mass to the powers 1/12, 5/24 and 5/8, respectively, consistent with earlier work by the author. Measurements are presented supporting the results. Physiological changes accompanying strenuous exercise are accounted for by a change in the scaling law for capillary number, from scaling exponent 5/8 to 3/4.

Mammalian basal metabolic rate is proportional to body mass2/3

The relationship between mammalian basal metabolic rate (BMR, ml of O(2) per h) and body mass (M, g) has been the subject of regular investigation for over a century. Typically, the relationship is expressed as an allometric equation of the form BMR = aM(b). The scaling exponent (b) is a point of contention throughout this body of literature, within which arguments for and against geometric (b = 2/3) and quarter-power (b = 3/4) scaling are made and rebutted. Recently, interest in the topic has been revived by published explanations for quarter-power scaling based on fractal nutrient supply networks and four-dimensional biology. Here, a new analysis of the allometry of mammalian BMR that accounts for variation associated with body temperature, digestive state, and phylogeny finds no support for a metabolic scaling exponent of 3/4. Data encompassing five orders of magnitude variation in M and featuring 619 species from 19 mammalian orders show that BMR proportional, variant M(2/3).

Allometric cascade: a model for resolving body mass effects on metabolism

Expanding upon a preliminary communication (Nature 417 (2002) 166), we here further develop a "multiple-causes model" of allometry, where the exponent b is the sum of the influences of multiple contributors to control. The relative strength of each contributor, with its own characteristic value of b(i), is determined by c(i), the control contribution or control coefficient. A more realistic equation for the scaling of metabolism with body size thus can be written as BMR=MR(0)Sigmac(i)(M/M(0))(bi), where MR(0) is the "characteristic metabolic rate" of an animal with a "characteristic body mass", M(0). With M(0) of 1 unit mass (usually kg), MR(0) takes the place of the value a, found in the standard scaling equation, b(i) is the scaling exponent of the process i, and c(i) is its control contribution to overall flux, or the control coefficient of the process i. One can think of this as an allometric cascade, with the b exponent for overall energy metabolism being determined by the b(i) and c(i) values for key steps in the complex pathways of energy demand and energy supply. Key intrinsic factors (such as neural and endocrine processes) or ecological extrinsic factors are considered to act through this system in affecting allometric scaling of energy turnover. Applying this model to maximum vs. BMR data for the first time explains the differing scaling behaviour of these two biological states in mammals, both in the absence and presence of intrinsic regulators such as thyroid hormones (for BMR) and catecholamines (for maximum metabolic rate).